Lyapunov stability theory for linear repetitive processes — The 1D equation approach

This paper reports further development of the so-called 1D Lyapunov equation based approach to the stability analysis of differential linear repetitive processes. In particular, it is shown that this approach leads to stability tests which can be implemented by computations with matrices which have constant entries, and that if the example under consideration is stable then physically meaningful information concerning one key aspect of `transient´ performance is available for no extra cost. The computational efficiency of these new stability tests against alternatives is also discussed and some areas for short to medium term further research briefly noted.